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Question 1 of 303.3333 PointsSolve the systemA.No .docx
- 1. Question 1 of 30 3.3333 Points Solve the system A. No solution B. x = 3, y = 2 C. x = 2, y = 5 D. E. x = 1, y = 2 Question 2 of 30 3.3333 Points In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 23 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner? (5280 feet in 1 mile.)
- 2. A. -13 ft B. 13 ft C. 3 ft D. -10 ft Question 3 of 30 3.3333 Points Write the partial fraction decomposition of the rational expression. A. + + B. + C. ++ D. ++ Question 4 of 30 3.3333 Points A flat rectangular piece of aluminum has a perimeter of 70
- 3. inches. The length is 11 inches longer than the width. Find the width. A. 34 inches B. 35 inches C. 23 inches D. 12 inches Question 5 of 30 3.3333 Points Solve the system of equations A. x = –1, y = 4, z = 1 B. x = –3, y = 7, z = 0 C. x = 4, y = 0, z = 0 D. x = –2, y = 2, z = -1 Question 6 of 30 3.3333 Points Ms. Adams received a bonus check for $12,000. She decided to divide the money among three different investments. With some
- 4. of the money, she purchased a municipal bond paying 5.8% simple interest. She invested twice the amount she paid for the municipal bond in a certificate of deposit paying 4.9% simple interest. Ms. Adams placed the balance of the money in a money market account paying 3.7% simple interest. If Ms. Adams' total interest for one year was $534, how much was placed in each account? A. municipal bond: $ 1500 certificate of deposit: $ 3000 money market: $ 7500 B. municipal bond: $ 2500 certificate of deposit: $ 5000 money market: $ 4500 C. municipal bond: $ 2000 certificate of deposit: $ 4000 money market: $ 6000 D. municipal bond: $ 1750 certificate of deposit: $ 3500 money market: $ 6750 Question 7 of 30 3.3333 Points Solve the system by the addition method. x2 - 3y2 = 1 3x2 + 3y2 = 15 A. {( 1, 2), ( -1, 2), ( 1, -2), ( -1, -2)}
- 5. B. {( 1, 2), ( -1, -2)} C. {( 2, 1), ( -2, 1), ( 2, -1), ( -2, -1)} D. {( 2, 1), ( -2, -1)} Question 8 of 30 3.3333 Points Solve the system of equations A. (19, -6) B. none of these C. (6, 19) D. (-6, -19) E. (19, 6) Question 9 of 30 3.3333 Points In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. Let x represent the number of years since 1990 and y represent the percentage of women in Milton Lake who smoke. The graph of y against x includes the data points (0, 15.9) and ( 13, 19.67). Let x represent the number of years since 1990 and y represent the percentage of men in Milton Lake who
- 6. smoke. The graph of y against x includes the data points (0, 29.7) and ( 15, 26.85). Determine when the percentage of women who smoke will be the same as the percentage of men who smoke. Round to the nearest year. What percentage of women and what percentage of men (to the nearest whole percent) will smoke at that time? [Hint: first find the slope- intercept equation of the line that models the percentage, y, of women who smoke x years after 1990 and the slope-intercept equation of the line that models the percentage, y, of men who smoke x years after 1990] A. 2019; 24% B. 2021; 24% C. 2023; 23% D. 2017; 25% Question 10 of 30 3.3333 Points Solve the system A. (-45, -9) B. (45, 9)
- 7. C. (9, 45) D. (45, -9) Question 11 of 30 3.3333 Points You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. A mathematical model can be used to describe the relationship for the ball's height above the ground, y, after x seconds. Consider the following data: x, seconds after ball is thrown y, ball's height, in feet, above the ground 1 114 2 146 4 114 Find the quadratic function y = ax2 +bx + c whose graph passes through the given points. A. y = -12x2 + 80x + 46 B. y = -10x2 + 60x + 64 C. y = -16x2 + 100x + 30
- 8. D. y = -16x2 + 80x + 50 Question 12 of 30 3.3333 Points Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 4x - 3y = 6 -12x + 9y = -24 A. {( 3, 4)} B. C. {(x, y) | 4x - 3y = 6 } D. ∅ Question 13 of 30 3.3333 Points A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 15 hours to paint, and 7 hours to fire. If the workshop has 116 hours for prep time, 64 hours for painting, and 110 hours for firing, How many of each can be made?
- 9. A. 8 wreaths, 6 trees, 2 sleighs B. 6 wreaths, 2 trees, 8 sleighs C. 9 wreaths, 7 trees, 3 sleighs D. 2 wreaths, 8 trees, 6 sleighs Question 14 of 30 3.3333 Points Solve the system by the substitution method. xy = 12 x2 + y2 = 40 A. {( 2, 6), ( 6, 2), ( 2, -6), ( 6, -2)} B. {( 2, 6), ( -2, -6), ( 2, -6), ( -2, 6)} C. {( 2, 6), ( -2, -6), ( 6, 2), ( -6, -2)} D. {( -2, -6), ( -6, -2), ( -2, 6), ( -6, 2)} Question 15 of 30 3.3333 Points Graph the solution set of the system of inequalities or indicate that the system has no solution. x2 + y2 ≤ 49
- 10. 5x + 4y ≤ 20 A. B. C. D. Question 16 of 30 3.3333 Points Find the determinant of the matrix. A. D = -277 B. D = -279 C. D = -276 D. D = -278 E. D = -272
- 11. Question 17 of 30 3.3333 Points Find the determinant of the matrix if it exists. A. 7 B. 27 C. -7 D. -9 E. 47 Question 18 of 30 3.3333 Points Give the order of the matrix, and identify the given element of the matrix. ; a12 A. 4 × 2; -11 B. 4 × 2; 14 C. 2 × 4; 14
- 12. D. 2 × 4; -11 Question 19 of 30 3.3333 Points Find the products AB and BA to determine whether B is the multiplicative inverse of A. A = , B = A. B = A-1 B. B ≠ A-1 Question 20 of 30 3.3333 Points Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. 3x + 5y - 2w = -13 2x + 7z - w = -1 4y + 3z + 3w = 1 -x + 2y + 4z = -5 A. {(-1, - , 0, )} B. {(1, -2, 0, 3)} C. {( , -2, 0, )}
- 13. D. {( , - , 0, )} Question 21 of 30 3.3333 Points Find the product AB, if possible. A = , B = A. B. C. D. AB is not defined. Question 22 of 30 3.3333 Points Find the products AB and BA to determine whether B is the multiplicative inverse of A. A = , B = A. B = A-1 B. B ≠ A-1 Question 23 of 30
- 14. 3.3333 Points Find the product AB, if possible. A = , B = A. B. C. D. AB is not defined. Question 24 of 30 3.3333 Points Solve the matrix equation for X. Let A = and B = ; 4X + A = B A. X = B. X = C. X = D. X =
- 15. Question 25 of 30 3.3333 Points Let A = and B = . Find A - 3B. A. B. C. D. Question 26 of 30 3.3333 Points Find the inverse of the matrix. A. B. C.
- 16. D. Question 27 of 30 3.3333 Points Determinants are used to show that three points lie on the same line (are collinear). If = 0, then the points ( x1, y1), ( x2, y2), and ( x3, y3) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (-2, -1), (0, 9), (-6, -21) and collinear? A. Yes B. No Question 28 of 30 3.3333 Points Use Cramer's rule to solve the system. 2x + 4y - z = 32 x - 2y + 2z = -5 5x + y + z = 20 A. {( 1, -9, -6)} B. {( 2, 7, 6)} C. {( 9, 6, 9)}
- 17. D. {( 1, 9, 6)} Question 29 of 30 3.3333 Points Find the product AB, if possible. A = , B = A. B. AB is not defined. C. D. Question 30 of 30 3.3333 Points Find the inverse of the matrix, if possible. A = A. B.
- 18. C. D.